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The University of Southampton
Mathematical Sciences

Research project: K-theory and cyclic homology of affine Weyl groups

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Affine and extended affine Weyl groups play a significant role in the classification of real and complex semi-simple Lie groups encoding the symmetries of their root and coroot lattices. Langlands duality is a duality between Lie groups which arises by interchanging roots and coroots, and this duality induces a duality at the level of the affine and extended affine Weyl groups. We showed that this duality is also related to the Baum-Connes isomorphism in K-theory, and in this project we are carrying out the explicit calculations necessary to understand this isomorphism, providing a whole new family of examples to illuminate the mysterious assembly map.

Having completed the study of the standard families Aₙ, Bₙ, Cₙ and Dₙ, we are now working on the exceptional cases.

Related research groups

Pure Mathematics
Noncommutative Geometry
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